Displaying similar documents to “On ( j , k ) -symmetrical functions”

Σ -isomorphic algebraic structures

Ivan Chajda, Petr Emanovský (1995)

Mathematica Bohemica

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For an algebraic structure = ( A , F , R ) or type and a set Σ of open formulas of the first order language L ( ) we introduce the concept of Σ -closed subsets of . The set Σ ( ) of all Σ -closed subsets forms a complete lattice. Algebraic structures , of type are called Σ -isomorphic if Σ ( ) Σ ( ) . Examples of such Σ -closed subsets are e.g. subalgebras of an algebra, ideals of a ring, ideals of a lattice, convex subsets of an ordered or quasiordered set etc. We study Σ -isomorphic algebraic structures in dependence...

Linear integral equations in the space of regulated functions

Milan Tvrdý (1998)

Mathematica Bohemica

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n this paper we investigate systems of linear integral equations in the space 𝔾 L n of n -vector valued functions which are regulated on the closed interval [ 0 , 1 ] (i.e. such that can have only discontinuities of the first kind in [ 0 , 1 ] ) and left-continuous in the corresponding open interval ( 0 , 1 ) . In particular, we are interested in systems of the form x(t) - A(t)x(0) - 01B(t,s)[d x(s)] = f(t), where f 𝔾 L n , the columns of the n × n -matrix valued function A belong to 𝔾 L n , the entries of B ( t , . ) have a bounded variation...

Essential norms of a potential theoretic boundary integral operator in L 1

Josef Král, Dagmar Medková (1998)

Mathematica Bohemica

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Let G m ( m 2 ) be an open set with a compact boundary B and let σ 0 be a finite measure on B . Consider the space L 1 ( σ ) of all σ -integrable functions on B and, for each f L 1 ( σ ) , denote by f σ the signed measure on B arising by multiplying σ by f in the usual way. 𝒩 σ f denotes the weak normal derivative (w.r. to G ) of the Newtonian (in case m > 2 ) or the logarithmic (in case n = 2 ) potential of f σ , correspondingly. Sharp geometric estimates are obtained for the essential norms of the operator 𝒩 σ - α I (here α ...